Identifiability in Dynamic Acyclic Networks with Partial Excitations and Measurements

TL;DR

This paper investigates conditions for identifying all modules in a dynamic acyclic network with partial measurements and excitations, proposing two sufficient criteria based on vertex analysis and graphical coverage.

Contribution

It introduces two new sufficient conditions for generic identifiability in acyclic networks with limited measurements and excitations, combining analytical and graphical methods.

Findings

First condition requires vertex-wise identifiability analysis.

Second condition uses tree/anti-tree covering for sensor and actuator placement.

Conditions enable guaranteed identifiability under partial data.

Abstract

This paper deals with dynamic networks in which the causality relations between the vertex signals are represented by linear time-invariant transfer functions (modules). Considering an acyclic network where only a subset of its vertices are measured and a subset of the vertices are excited, we explore conditions under which all the modules are identifiable on the basis of measurement data. Two sufficient conditions are presented in the paper, where the first condition concerns an identifiability analysis that needs to be performed for each vertex, while the second condition, based on the concept of tree/anti-tree covering, results from a graphical synthesis approach to allocate actuators and sensors in an acyclic network for achieving generic identifiability.